How to prove the coordinate axes (x-axis &y -axis )mutually perpendicular to each other algebraically. ?
The slope of one line is tan(theta) where theta is the angle with the x axis. The slope of the perpendicular line is -1/tan(theta). The product is -1 whenever both tan(theta) or 1./tan(theta) are finite; otherwise it doesn't make sense. The better way to check for perpendicularity is to check the dot product, which is zero for the x and y axes.